F(x)=-100x^2+1900x-6000

Solution for F(x)=-100x^2+1900x-6000 equation:

(F)=-100F^2+1900F-6000

We move all terms to the left:

(F)-(-100F^2+1900F-6000)=0

We get rid of parentheses

100F^2-1900F+F+6000=0

We add all the numbers together, and all the variables

100F^2-1899F+6000=0

a = 100; b = -1899; c = +6000;
Δ = b2-4ac
Δ = -18992-4·100·6000
Δ = 1206201
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1899)-\sqrt{1206201}}{2*100}=\frac{1899-\sqrt{1206201}}{200}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1899)+\sqrt{1206201}}{2*100}=\frac{1899+\sqrt{1206201}}{200}
$